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break Review of periodicity: Periodicity refers to the observed trends of various atomic properties of the elements with respect to their position in the periodic table. An understanding of periodicity is one of the most important and useful concepts in understanding chemical behavior in minerals. Periodicity of size: Atomic radius increases significantly from top to bottom, e.g. H, Li, Na, K, Rb, Cs and Fr. The addition of an extra period (row) means those new electrons orbitals are further from the nucleus. Atomic radius decreases slightly from left to right, e.g. Na, Mg, Al, Si, P, S, Cl, Ar. This may seem counter-intuitive, because one would think that adding extra electrons would increase the atomic size rather than decrease it. But because the new electron orbitals are in the same period as the preceding element, they are not that much different in distance to the nucleus. And because the nuclear charge has also increased (with the addition of more protons), all of the electrons are drawn in slightly closer. Ionic radius increases significantly from top to bottom, e.g. H +, Li +, Na +, K +, Rb +, Cs + and Fr +. The addition of an extra period (row) means those new electrons orbitals are further from the nucleus. The removal of the valence electrons (to make cations) decreases an element's ionic radius relative to its atomic radius, but the trend remains the same. Ionic radius decreases from left to right for an isoelectronic series, e.g. Na +, Mg 2+, Al 3+, Si 4+, P 5+, S 6+ and Cl 7+. This trend is more pronounced than the atomic trend because of the increasing effect of the nuclear charge on the remaining electrons. Ionic radius decreases with increasing charge for a given element, e.g. Cl -, Cl +, Cl 3+, Cl 5+ and Cl 7+. Again, this trend is a consequence of a given nuclear charge having a greater pull on fewer electrons. Note that if electrons are added to the element rather than removed (i.e. Cl - ), the ion becomes larger than the atom. Hence, anions are generally relatively large, and cations are generally relatively small. Based on these observations, how would the REE 3+ trend from La 3+ to Lu 3+? Going further, how would Ce 4+ (in oxidized environments) or Eu 2+ (in more reduced environments) compare to Ce 3+ and Eu 3+, respectively, and also to their adjacent REE 3+ neighbors? The ability of Ce to be 3+ or 4+, and of Eu to be 3+ or 2+, and the fact that the sizes of these less common valences are notably different from the general REE 3+ trend has important implications for petrogenesis. ------------------------------------------------------------------------------------------------------------------------------------ Periodicity of charge: Students sometimes have a difficult time remembering the typical valences of the common elements. But there are some simple trends that can help with learning these. Cation charges trend this way: group 1 (the "alkali metals" and H) is the first column and these elements are always 1+ in nature.

group 2 (the "alkaline-earth metals") is the second column and these elements are always 2+ in nature. if we skip the transition metals for the moment, group 3 (the boron-aluminum group) is the third main column and these elements are usually 3+ in nature (there are exceptions lower down in the column, where 1+ is observed... e.g. Tl + is much more abundant than Tl 3+ ). group 4 (the carbon-silicon group) is the fourth main column and these elements are usually 4+ in nature (there are exceptions lower down in the column, where 2+ is observed... as with Tl, Pb 2+ is more common than Pb 4+ ; we're also far enough to the right on the periodic table that anion charges become a bit more important, but only for carbon). group 5 (the nitrogen-phosphorus group) is the fifth main column and these elements are usually 5+ in nature (for example, P 5+ in phosphate). But 3+ can also be important for these elements, especially lower down in the column, and anion behavior is also increasingly more important, especially near the top. group 6 (the oxygen-sulfur group) is the sixth main column. The geologically important members (particularly O and S) are usually anions (O 2- and S 2- ), but S in sulfate is 6+, and more rarely can also be other valences such as 4+. group 7 (the halogens) is the seventh main column. Other than a few extremely rare exceptions, the elements are always 1- anions in nature. In the lab, however, valences of 1+, 3+, 5+ and even 7+ are not uncommon. Returning to the transition metals, here the column represents the maximum valence a transition metal can be (up to 8), but valences of 2+ and 3+ are the most common in important rock-forming minerals: the 3rd column (headed by Sc): always 3+ in nature. the 4th column (headed by Ti): essentially always 4+ in nature (on Earth; on the Moon and in some similar very reduced environments Ti 3+ may occur). the 5th column (headed by V): usually 3+ in nature near the top of the column (e.g. V 3+ in FeV 2O 4), or 5+ near the bottom of the column (Nb 5+ and Ta 5+ in columbite-tantalite) or in near-surface oxidizing environments (e.g. V 5+ in vanadinite). Rarely V can be 4+ (e.g. when V 4+ substitutes for Ti 4+ in titanite), but this is uncommon. the 6th column (headed by Cr): usually 3+ in nature near the top of the column (e.g. Cr 3+ in FeCr 2O 4), or 4+ to 6+ near the bottom of the column (e.g. Mo 4+ in molybdenite and Mo 6+ and W 6+ in powellite-scheelite) or rarely in near-surface oxidizing environments. The infamous "hexavalent chromium" environmental toxin brought to light in the movie "Erin Brockovich" is Cr 6+, but in this instance was man-made. Natural Cr 6+ essentially occurs only in the spectacular orange mineral crocoite (PbCrO 4), popular with collectors. the 7th column (headed by Mn): usually 2+ (e.g. Mn 2+ in rhodonite, MnSiO 3) in most minerals, and somewhat less commonly 3+ (e.g. Mn 3+ in manganite, MnO(OH)) or 4+ (e.g. Mn 4+ in pyrolusite, MnO 2) near the top of the column, or 4+ to 7+ near the bottom of the column (e.g. Re 4+ in the sulfide rheniite, but Re 7+ in ReO 4 - ion). Mn 7+ is the violet ion in potassium permanganate (a household antiseptic), but is too oxidized to occur in nature. the 8th, 9th and 10th columns (headed by Fe, Co and Ni; the "iron" block): usually 2+ or 3+ in nature near the top of the column (Fe 3+ is common, but Co 3+ and Ni 3+ are uncommon; Co 2+ and Ni 2+ are more typical), or 2+ or 4+ near the bottom of the column. 8+ is possible in the lab, even for Fe, but is too oxidized to occur in nature for any of the group. A valence of 0 is also common, especially

for the elements in the platinum group; this is less common for Fe, Co and Ni, but iron meteorites are a good example of native iron-nickel (essentially Fe 0 ). the 11th column (headed by Cu): Cu is 0, 1+ or 2+ (Cu 2+ is most typical in silicates and many oxides), Ag is 0 or 1+ (in sulfides), and Au is almost always 0 but may rarely be 1+ (or 3+ in the lab). the 12th column (headed by Zn): essentially always 2+, but Hg can be 0 or 1+ as well. group 8 (the noble gases) are always 0 in nature and form no minerals. He and Ar may be found trapped in minerals (because they can form from radioactive decay of U and K, respectively), but in general the noble gases are restricted to the atmosphere. ------------------------------------------------------------------------------------------------------------------------------------ Periodicity of coordination number (C.N.): Coordination number is the number of nearest atomic neighbors surrounding an atom of interest. Although we can talk about coordination number around atoms (for example, CCP and HCP in metals) or the coordination number around anions (for example, noting the analogous packing of 6 Cl - around Na + and 6 Na + around Cl - in halite), we're generally the most interested in the packing of anions (usually O 2- ) around cations. Understanding coordination number is very important in mineralogy and petrology, because in addition to the size of the ion, coordination number is influenced notably by pressure and to a lesser degree by temperature. Coordination numbers are usually represented by a roman numeral superscript preceding the element or crystallographic site of interest: VIII ZrSiO 4 (Zr is 8-coordinated in zircon). For a given set of P-T conditions, increasing atomic radius tends to increase the C.N. Hence, for the alkaline-earth carbonates at near surface conditions, we observe VI MgCO 3, VI CaCO 3 (most commonly), but then IX SrCO 3 and IX BaCO 3. Changes in P result in the most marked changes in coordination number. Increasing pressure allows more anions to be crowded around a cation, and so C.N. goes up. Important examples include: III C (graphite) goes to IV C (diamond) with increasing P. VI CaCO 3 (calcite) goes to IX CaCO 3 (aragonite) with increasing P, although aragonite can also occasionally form in near-surface environments thanks to lowered kinetic barriers. IV SiO 2 (quartz) goes to VI SiO 2 (stishovite) with increasing P (on Earth that typically means instantaneous high-p shock metamorphism from a meteorite impact). Changes in T tend to have a smaller and less clear impact on coordination number than does P. Other less common properties, such as crystal field stabilization energies of certain transition metal ions, also affect coordination number. Coordination number examples (note the various periodic trends): III (trigonal): group 3: III B 3+ in tourmaline group 4: III C 4+ in carbonates and graphite

IV (tetrahedral): group 5: III N 5+ in nitrates group 2: IV Be 2+ in beryl and most Be-bearing minerals; IV Mg 2+ in spinel and melilite group 3: IVI B 3+ in many borates and borosilicates; IV Al 3+ in feldspar and many other Al-bearing minerals group 4: IV C 4+ in diamond; IV Si 4+ in essentially all crustal silicates group 5: IV P 5+ in apatite and other phosphates; IV As 5+ in arsenates transition metals: IV Fe 2+ and rarely IV Co 2+ in staurolite and some oxides; IV Zn 2+ in sphalerite and willemite; many small higher charge ions are also IV (e.g. IV V 5+ in vanadates, IV Mo 6+ in molybdates, IV W 6+ in tungstates). IV (square planar): not common; usually seen in some Pt and Pd minerals. V: one of the two Al in andalusite, but otherwise not common. VI (octahedral and other geometries): group 1: VI Li + in tourmaline, micas, chlorite and some amphiboles VI Na + in halite group 2: VI Mg 2+ in olivine and many other Mg-bearing minerals; VI Ca 2+ in calcite group 3: VI Al 3+ in corundum, spinel, garnet, tourmaline, jadeite, kyanite and many other Al-bearing minerals group 4: VI Si 4+ in stishovite and some other deep mantle silicates (only one crustal mineral with VI Si 4+ [thaumasite] is known); VI Sn 4+ in cassiterite VI Pb 4+ in plattnerite (an oxide) VI Pb 2+ in galena (a sulfide) transition metals: many transition metal ions ( VI Ti 4+, VI V 3+, VI Cr 3+, VI Mn 2+, VI Mn 3+, VI Fe 2+, VI Fe 2+, etc.) in a variety of minerals such as amphibole, pyroxene, mica, epidote, tourmaline, olivine, as well as in carbonates, phosphates, some sulfides, etc. VII: VII Ca 2+ in titanite, but otherwise not common. VIII (body-centered cubic and other geometries): group 1: VIII Li + in pyroxene and some amphiboles VIII Na + in pyroxene and some amphiboles group 2: VIII Mg 2+ in garnet and the M4 site of some Mg-rich amphiboles; VIII Ca 2+ in fluorite, garnet, pyroxene and amphibole transition metals: VIII Fe 2+ and VIII Mn 2+ in garnet and in some Fe±Mn-rich amphiboles; VIII Y 3+ in xenotime; VIII Zr 4+ in zircon. REE and actinides: VIII REE 3+ in xenotime; VIII Th 4+ in thorianite and thorite; VIII U 4+ in uraninite.

IX: group 2: IX Ca 2+ in aragonite and one site in epidote; IX Sr 2+ in strontianite and one site in epidote; IX Ba 2+ in witherite group 4: IX Pb 2+ in cerussite; REE and actinides: IX REE 3+ and IX Th 4+ and IX U 4+ in monazite. XII (dodecahedral [edge-centered cubic] and other geometries): group 1: XII Na + in tourmaline, mica and the A site in some amphiboles; XII K + in mica and the A site in some amphiboles; XII Rb + in mica; XII Cs + in mica group 2: XII Mg 2+ in mantle "perovskite" ("MgSiO 3"); XII Ca 2+ in perovskite (CaTiO 3), tourmaline and mica; XII Sr 2+ in celestite XII Ba 2+ in mica and barite group 3: XII Tl + substituting for XII K + in comparable minerals; group 4: XII Pb 2+ in amphibole large variable-sized cages and channels (VI and larger): Na +, Ca 2+, K + in feldspar, scapolite, nepheline and other framework silicates; alkali metals and H 2O in beryl; alkali metals, H 2O and CO 2 in cordierite; Cl -, S 2-, CO 3 2-, SO 4 2-, S 3 2- in feldspathoids; a variety of species (even large organic polyatomic groups such as N[CH 3] 4 + ) in zeolites. Review of the main silicate structural units (these six "skeleton" formulas cover all of Bowen's reaction series and many metamorphic minerals): [TO 4] [T 2O 6] [T 8O 22](OH) 2 [T 4O 10](OH) 2 [T 4O 10](OH) 8 [T 4O 8] As an example, we can use the [T 4O 8] skeleton formula to start with quartz and derive the feldspars As a more complex example, we can use the [T 4O 10](OH) 2 skeleton formula to start with talc and derive pyrophyllite and the micas.